Assume the representative consumer lives in two periods and his preferences can be described

by U(c, c')=c^(1/2)+(c')^(1/2)

where c is the current consumption, c' is next period consumption, and = 0.95. Let's assume that the consumer can borrow or lend at the interest rate r = 10%. The consumer receives an income y = 100 in the current period and y' = 110 in the next period. The government wants

to spend G = 30 in the current period and G' = 35 in the future period.

1. Solve the consumer's problem by finding the optimal allocations c^* and c^(l*). [10 points]

2. Is the economy at the equilibrium? Explain. [05 points]

3. What are the equilibrium values of c and c'? [05 points]

4. What is the equilibrium interest rate? [05 points]

5. How will the equilibrium interest rate respond to an increase in G? [05 points]

6. How will the equilibrium interest rate respond to an increase in G'? [05 points]